who wants to build a warp drive anyway?

November 4, 2009

Usually, when I post about a scientific paper, the focus is on its methodology and interpreting its conclusions into real world applications. This time, we’re going to do something a little different and use an oft cited paper on the plausibility of warp drive propulsion to build a theoretical model of our own. You see, when physicists Richard Obousy and Gerald Cleaver put together the energy requirements for a warp drive, they noted that a sufficiently advanced civilization could one day build it. And we’re going to use those requirements to find out whether a civilization like that could conceivably exist and what would happen to their solar system if they ever tried to create a device that warps space and time by locally boosting the ongoing expansion of the universe.

So how much energy does it take to get a warp drive revving? A jaw dropping 1042 J / m3 which is like taking a planet a bit more massive than Saturn, crushing it into a cube about the size of a nightstand and turning all of that into raw, pure energy. Do that, say Obousy and Cleaver, and you effectively start changing the value of the cosmological constant, the Λ in Einstein’s general relativity equations. Each time you do that, you’ll get a cubic meter of warped space-time which will propel your ship forward at the speed of light. This is the kind of energy output that our hypothetical alien race interested in superluminal travel would have to meet to get then within a whisker of their goal. We’ll have to assume that they’re tens of thousands of years ahead of us in science and technology, and have an industrial capacity we could only dream of for the foreseeable future. Otherwise, any chance of them building any kind of warp device would be nil.

For the sake of argument, let’s get our aliens started with a more or less conventional approach. To pinch the fabric of space and time, they’re going to have to build an enormous bomb that will essentially implode into a cubic meter of warped space-time. Why a bomb? Because this energy would have to be delivered in a burst, or it will simply dissipate. Even though it sounds like a lot, the energy requirement we’re dealing with isn’t that much on a cosmic scales. Supernova explosions give off far more energy which simply spreads through their galaxy in a bubble measuring light years across. We want to take all those Joules and focus them on the area of space-time we want to manipulate. So how big would the bomb have to be when we use a technology that both we and our advanced aliens would know very well?

One of the most powerful explosive designs we’ve created was the Tsar Bomba which was initially built with a stunning 100 megaton yield that was later reduced due to concerns over widespread fallout. But let’s say that our aliens build an explosive sphere of staged thermonuclear devices with the full intended yield and with the same size and density. If we run through a quick blizzard of math, we’ll come up with a device that should be the stuff of nightmares for just about any intelligent species. It would be 7.5 billion km across and tip whatever monster scales you’d use to measure it at 50 quintillion metric tons. In other words, it would be roughly as big as a solar system and have a mass comparable to Mars. Clearly that’s not a very practical project since even at a rate of a million bombs a year, the giant device would take some 2.3 quintillion years to complete and the result wouldn’t be a reusable method of propulsion for a fleet of spacraft. Oh and by the way, those quintillions of years are longer than the lifetime of our current phase of the universe. The very last star would’ve died eons before the bomb is built and ready to go. Clearly, we’re not off to a good start here.

Luckily for us and our hypothetical aliens, Obousy and Cleaver provide an alternative in the form of 1028 kg of antimatter which could be used to generate more than enough power for a warp bubble accommodating one spacecraft with a volume of a cubic kilometer. Unfortunately that’s not a great alternative either. If we take half of that antimatter and come up with a chunk of matter just as huge, then collide them, we’ve effectively made a doomsday machine that would wipe out our hypothetical alien species. When matter and antimatter collide in an explosive reaction, they emit a flood of gamma rays. The ionizing radiation from the equivalent of blowing up Jupiter could easily decimate life in the solar system where the device is being built by triggering horrifying mass extinctions and changing the chemical structure of previously habitable atmospheres. It would be like a gamma ray burst from a hypernova and it doesn’t seem very likely that any civilization could survive triggering one in their own backyard. Besides, the sheer mechanics of assembling this much matter would be easily on par with the bomb scenario and whatever species started the project would be extinct long before completing it. Even boosting production rates by thousands of times wouldn’t help.

Finally, let’s go back to the initial requirements and consider what a density of 1042 J / m3 actually means. By converting this energy to mass, we’ll see that it far exceeds the density of the core of a neutron star. And since neutron stars are as dense as matter can get until it collapses into a black hole, anything that would create a similar energy density could essentially create a black hole about 33 meters across with an expected lifetime of 3.6 × 10^60 years if it recreated the conditions needed for Obousy and Cleaver’s theoretical spacecraft to hit the speed of light. To escape the shockwave and be able to aim the GRB far enough away, the civilization that created this black hole machine would have to build it hundreds of millions of miles away from the planet it would occupy. Though, as we saw already, any civilization capable of building a black hole machine would be living in a cold, dark universe lit by embers of old, dead stars slowly simmering away into dense, solid matter, even if it started working on the project now. And in my humble opinion, such an advanced species would find other things to do with its time or just opt to make the best out of relativistic rocketry to get around.

So obviously you don’t share, and have probably never heard of, the basic technological assumptions that underlie this sort of megaengineering problem. Nobody’s doing this stuff by making bombs on an assembly line, and nobody’s doing this stuff around fleshbags on planets who would indeed be vaporized by a hypernova-type event in their backyard. This is about future industry, which is not a bigger and better version of present-day industry, it is about replicating nanomachinery at the molecular or smaller level, and minds who aren’t running on watery proteins held together by van der Waals forces. This is the posthuman era, long after flesh and far beyond steel.

The last paragraph, though, shows major errors of the underlying science, which is a very different matter than failure to share the sort of implicit technological assumptions that are being talked about.

Neutron star density is not black hole density. Period. Black hole density (not just volume) depends on the mass, and a black hole the size of the Sun would be 3 km across. A Jupiter-mass black hole would be 6m across, and Obousy and Cleaver talked about putting that mass into a 10m cube, which is fine. (And that’s a thousand cubic meters, not a cubic kilometer!)

That’s the sort of thing that Obousy and Cleaver would have noticed immediately, and the referees would have seen it if they didn’t. You should have questioned your own belief that a published journal article would contain a mistake that obvious. As it is, I’m afraid this article is very much the analogue of chiding Goddard for believing that rockets can operate in space without something to push against. The gross errors of math and science are yours, not Obousy’s and Cleaver’s.

Retract this blog post and start over.

Greg Fish

“Neutron star density is not black hole density. Period.”

No it’s not. But when you exceed neutron star density, you get a complete collapse of the object since it’s being held together by degenerate pressure. And that collapse is what we know as a black hole. The word “similar” referred to the energy density of the warp drive requirements, not of a neutron star. Sorry if this wasn’t clear at first.

“A Jupiter-mass black hole would be 6m across…”

Well, 5.6 m actually. But then again, we’re not calculating a Jupiter mass black hole. Instead, we’re looking at the mass represented by 10^45 J in a cubic meter, so the resulting equation will look like this:

rs = 2G(1.11 × 1028) / c2 = 16.4784 m

Where G is 6.673 × 10-11, so if we multiply the Schwatzschild radius by two, we get a diameter of 32.9568 m which we can pretty safely round up to 33 meters.

“…and [the authors] talked about putting that mass into a 10m cube, which is fine.”

The paper makes no mention of making a black hole and putting it into a 10 meter cube. If you note how they came up with the energy requirements for the warp drive, they used a spacecraft with a volume of 1,000 cubic meters and multiplied that by the energy density needed to increase the Λ value in the following manner on page 11…

Vcraft = 10 m × 10 m × 10 m = 1000 m3
Ec = Λc × Vcraft = 1045 J

Also how is it fine to create a black hole and stuff it in a cube? And wouldn’t it make sense that warp drive makers trying to create an extremely high energy density in a small area of space might just create a black hole?

“You should have questioned your own belief that a published journal article would contain a mistake that obvious.”

Err… the post assumes that Obousy and Cleaver were correct which is why it uses the numbers and figures they provided without question. I said absolutely nothing about the paper containing any mistakes. They found the energy requirements. I tried to use their results to figure out who could meet them.

“Retract this blog post and start over.”

Sure. Any other posts that you’d like me to remove or edit to your standards? After all, it’s not like it’s my blog or anything… < /sarcasm>

I’m wondering what would happen if a ship ” lassoed” (ignoring the science of that) a tachyon, that was going the speed of light or faster and the ship was able to withstand the resulting force. Would it be able to “hold onto it, or would it implode or something else spectacularly messy?

Greg Fish

“what would happen if a ship ” lassoed” a tachyon going the speed of light or faster”

By definition, a tachyon would have to travel faster than light. But the problem with that is the very simple fact that it would violate the maximum speed in space-time and be instantly destroyed according to the laws of physics.

Likewise, it would be pretty hard to catch a particle comparable to an atom in space. Your best shot would be to put out a collection shield, have the particle collide with it and stop its motion with the overwhelming mass of your spacecraft.

http://enlighternmentjunkie.wordpress.com Mithy

Neutron star density is not black hole density. Period. Black hole density (not just volume) depends on the mass, and a black hole the size of the Sun would be 3 km across. A Jupiter-mass black hole would be 6m across, and Obousy and Cleaver talked about putting that mass into a 10m cube, which is fine. (And that’s a thousand cubic meters, not a cubic kilometer!)

Eliezer, you do actually know that when Greg talks about the “sizes” of black holes he’s actually talking about the radius of the event horizon, which is merely (hah!) the location where the escape velocity is => c. And if we’re talking about a civilisation that has the means to stick a black hole in a box, they’ve probably got the means of shielding the black hole sufficiently so that the Schwartzchild radius is effectively immateral. Black holes, or rather the singularity themselves have, according to GR, infinite density since they, as far as we can understand, have zero volume. So moaning about radius/density is rather irrelevant, to be honest.

You appear to lack the understanding yourself that you accuse others of.

By definition, a tachyon would have to travel faster than light. But the problem with that is the very simple fact that it would violate the maximum speed in space-time and be instantly destroyed according to the laws of physics

This is wrong. The whole idea of tachyons arose from the observation that they are in fact consistent with the solutions to special relativity. They have to have some very weird properties, such as having imaginary “rest mass” but there’s nothing that shows that they would have to be “instantly destroyed.”

rob k

what if you could some how take the mass from are ship and make it zero then the energy needed to move would be less, kinda of like a photon of light